Answers
The numbers to complete the pythagorean triple in the equation (n² - 1)² + k² = (n² + 1)² are B. 35 and 37
What is the pythagorean triple?A pythagorean triple is a set of 3 numbers that obey the pythagorean theorem.
Given the equation
(n² - 1)² + k² = (n² + 1)², we need to find the remaining numbers generated by the equation when k = 12. So, we proceed as follows/
Since we have the equation
(n² - 1)² + k² = (n² + 1)²
Subtracting (n² + 1)², from both sides, we have that
(n² - 1)² - (n² + 1)² + k² = (n² + 1)² - (n² + 1)²
(n² - 1)² - (n² + 1)² + k² = 0
Now, subtracting k from both sides, we have that
(n² - 1)² - (n² + 1)² + k² = 0
(n² - 1)² - (n² + 1)² + k² - k² = 0 - k²
(n² - 1)² - (n² + 1)² + 0 = - k²
(n² - 1)² - (n² + 1)² = - k²
Using the difference of two squares a² - b² = (a + b)(a - b)
(n² - 1)² - (n² + 1)² = - k²
(n² - 1 + n² + 1)[n² - 1 - (n² + 1)] = - k²
(n² + n² - 1 + 1)[n² - n² - 1 - 1)] = - k²
(2n² + 0)[0 - 2)] = - k²
(2n²)(- 2) = - k²
-4n² = - k²
4n² = k²
n² = k²/4
Taking square root of both sides, we have that
n = √(k²/4)
n = k/2
Since k = 12, we have that
n = 12/2
n = 6
So, the first number is (n² - 1) = (6² - 1)
= 36 - 1
= 35
The second number is (n² + 1) = (6² + 1)
= 36 + 1
= 37
So, the numbers are B. 35 and 37
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Related Questions
A Ferris wheel has a diameter of 60 m, with a minimum height of 9 m above the
ground. It takes 20 seconds for the Ferris wheel to complete one rotation. If a rider
boards a car when it is at its lowest point
O: What is the minimum height of the rider?
A: Minimum height of the rider is __ meters.
No Links Or I’ll Report You
Answers
By knowing geometrical dimensions, the minimum height of the rider in the Ferris wheel, modeled by a sinusoidal function, is equal to a height of 9 meters.
How to analyze a Ferris wheel
The model of the height of a Ferris wheel is represented by a sinusoidal model, which is presented below:
h = A + B · sin ωt (1)
Where:
A - Midpoint height, in meters. B - Amplitude, in metersω - Angular frequency, in radians per second.t - Time, in secondsSinusoidal functions are bounded functions, the minimum height of the Ferris wheel represents the lower bound of the function and the maximum height is the upper bound. Therefore, the minimum height of the rider is:
\(h_{min} = 39\,m - 30 \,m\)
\(h_{min} = 9\,m\)
By knowing geometrical dimensions, the minimum height of the rider in the Ferris wheel, modeled by a sinusoidal function, is equal to a height of 9 meters.
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Hey guys can you please help me out with my math homework
Answers
Answer:
I Think its 81.68141
Fluency in the conversion of the metric system to the Imperial System is an essential skill in the nursing profession. Think of a situation in which negative effects have occurred due to incorrect dosage calculations? This situation could be a personal experience, the experience of someone you know, or a hypothetical. Explain how this error could have been avoided. How will you ensure that you avoid dosage errors due to metric conversions in your future career as a nurse?
Answers
In a hypothetical situation, an incorrect dosage calculation due to an error in metric system to Imperial System conversion could lead to potential harm to the patient. To avoid such errors, it is crucial to ensure accurate and precise conversions between the metric and Imperial systems. As a nurse, I will double-check my calculations, use reliable conversion charts or tools, and consult with colleagues or supervisors when in doubt. Additionally, ongoing education and training on dosage calculations and metric system conversions will be important to maintain proficiency and prevent errors in the future.
~~~Harsha~~~
Help please...............
Answers
eu (european union) countries report that 46% of their labor force is female. The United Nations wnats to determine if the percentage of femailes in the U.S. labor force is the same. Based on sample, representatives from the United States department of labor find that the 95% confidence interval for the proportion of females in the U.S. labor force is .357 to .443. if the department of labores wishes to tighten it's interval they should
Answers
Answer:
Step-by-step explanation:
The question is incomplete. The complete question is:
EU (European Union) countries report that 46% of their labor force is female. The United Nations wants to determine if the percentage of females in the U.S. labor force is the same. Based on a sample of 500 employment records, representatives from the United States Department of Labor found that the 95% confidence interval for the proportion of females in the U.S. labor force is 0.357 to 0.443. If the Department of Labor wishes to tighten its interval, they should:
A. increase the confidence level
B. decrease the sample size
C. increase the sample size
D. Both A and B
E. Both A and C
Solution:
Confidence interval for population proportion is written as
Sample proportion ± margin of error
Where sample proportion is the point estimate for the population proportion.
Margin of error = z × √pq/n
The z score for 95% confidence level is 1.96
p = 46/100 = 0.46
q = 1 - p = 1 - 0.46
q = 0.54
n = 500
Margin of error = 1.96√0.46 × 0.54/500 = 0.044
To tighten it's interval, the margin of error needs to be reduced.
If we increase the confidence level, say to 99%, z = 2.58
Then
Margin of error = 2.58√0.46 × 0.54/500 = 0.058
It increased
Also, If we increase the sample size, say to 700, then
Margin of error = 1.96√0.46 × 0.54/700 = 0.037
It has reduced
Therefore, the correct options is
C. increase the sample size
Hi please help on question! . If answer is correct I'll rate you five stars a thanks and maybe even brainliest! You will even get 39 pts!!
Here is a function machine.
Input : multiply by 6. Subtract 80: output
The input is the same as the output. Find the input.
Also can you please show me an easy to work out these type of questions
Answers
The input (x) that satisfies the condition of being multiplied by 6 and then Subtracted by 80 to give the same value as the output is 16.
The input as "x." According to the given information, the input (x) is multiplied by 6 and then subtracted by 80, resulting in the output. In mathematical terms, this can be expressed as:
Output = (6 * x) - 80
The problem states that the input and output are the same. Therefore, we can set up the equation:
x = (6 * x) - 80
To solve for x, we'll rearrange the equation and isolate the variable:
x - 6 * x = -80
Combine like terms:
-5 * x = -80
Divide both sides by -5:
x = (-80) / (-5)
Simplifying the division:
x = 16
Hence, the input (x) that satisfies the condition of being multiplied by 6 and then subtracted by 80 to give the same value as the output is 16.
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Which of the following shows numbers ordered from least to greatest
Answers
Answer:
A
Step-by-step explanation:
It is option A: -2, -1, 0, 1
Someone HELPPppp for tmr
Answers
Answer:
y=1x-6
Step-by-step explanation:
First we find the slope by using rise over run. So you can either count up and over(rise/run) or use the slope formula y2-y1/x2-x1. You will find that the slope is 1, so plug that into the equation for mx. So we have y=1x so far. Then we find the y-intercept by looking where the graph intersects the y-axis. As you can see it intersects at -6, so plug -6 into the equation for b. No we have our full equation of y=1x-6.
-Hope this helped
Solve b + 6 < 14.
Write your answer in set builder notation
Answers
b + 6 - 6 < 14 - 6
This simplifies to:
b < 8
Therefore, the solution to the inequality is the set of all numbers b that are less than 8.
In set builder notation, we can represent this solution as:
{ b | b < 8 }
Hank made payments of $219 per month at the end of each month for 30 years to purchase a piece of property. He promptly sold it for $195,258. What interest rate, compounded monthly, would he need to earn on an ordinary annuity for a comparable rate of return?
Answers
To achieve a comparable rate of return, Hank would need to earn an interest rate of approximately 0.86% per month, compounded monthly on his ordinary annuity.
To find the interest rate, compounded monthly, that Hank would need to earn on an ordinary annuity for a comparable rate of return, we can use the present value formula for an ordinary annuity.
First, let's calculate the present value of Hank's payments. He made payments of $219 per month for 30 years, so the total payments amount to $219 * 12 * 30 = $78840.
Now, we need to find the interest rate that would make this present value equal to the selling price of the property, which is $195,258.
Using the formula for the present value of an ordinary annuity, we have:
PV = P * (1 - (1+r)\(^{(-n)})\)/r,
where PV is the present value, P is the payment per period, r is the interest rate per period, and n is the number of periods.
Plugging in the values we have, we get:
$78840 = $219 * (1 - (1+r)\({(-360)}\))/r.
Solving this equation for r, we find that Hank would need to earn an interest rate of approximately 0.86% per month, compounded monthly, in order to have a comparable rate of return.
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marian has a savings account with $21,390 if she earns $4,100 per month, what is the maximum she can spend on a house?
Answers
The answer is: 4100x + 21390
We need to know the number of months Marian wants to save to get the specific value.
Step-by-step explanation:
In the equation, we will need to calculate the maximum amount of money Marian can spend on the house.
We can calculate the maximum amount of money Marian can spend on a house by multiplying her monthly income by the number of months she would want to save.
Solve the problem:Marian earns $4,100.00 per month
Suppose Marian wants to save for x months, then the maximum amount that she can spend on the house is:
4100 * x + 21390
Draw the conclusion:The answer is: 4100x + 21390
We need to know the number of months Marian wants to save to get the specific value.
Hope this helps!
Use ratio language to describe the relationship of any two things you can think of.
make this answer resonable and i will mark you brainliest
thanks
Answers
Answer:
Step-by-step explanation:
the recipe called for 3 cups of flour and 4 cups of sugar. That means there is 3/4 cups of flour for each cup of sugar.
She drove 60 miles in 3hrs. This means she drove 60/3 = 20 miles per hr.
hope this helps?
Pls help do you know 500000x4000000000➗4
Answers
Answer:
500000000000000
Step-by-step explanation:
multiply 500000 by 4000000000 (2000000000000000), then divide by 4 (500000000000000)
5x-3(-5y+6x) +4y i need help please
Answers
To simplify the expression \(\displaystyle\sf 5x-3(-5y+6x)+4y\), we can follow the order of operations, which involves simplifying the expressions within parentheses, applying the distributive property, and combining like terms.
Using \(\displaystyle\sf \) tags for formatting, the expression becomes:
\(\displaystyle\sf 5x-3(-5y+6x)+4y\)
First, we simplify the expression within the parentheses:
\(\displaystyle\sf 5x-3(-5y+6x)+4y\)
\(\displaystyle\sf 5x+15y-18x+4y\)
Next, we can combine the like terms:
\(\displaystyle\sf 5x-18x+15y+4y\)
\(\displaystyle\sf -13x+19y\)
Therefore, the simplified expression is \(\displaystyle\sf -13x+19y\).
\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)
♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)
Find f(3) and interpret its meaning.
Answers
Answer:
f(3) = 425
f(3) is the elevation of a mountain climber after 3 hours of climbing.
Step-by-step explanation:
So we are given a line that relates time to elevation. We are also given that the equation of the line is f(x) = 125x + 50. From looking at the graph given, we can see that x is the time, in hours, and y, or f(x), is the height, in feet. We are asked to find f(3) and interpret it's meaning.
To find f(3), we would have to find what f(x) is when x = 3. To do this, lets plug in 3 for x into the given equation:
f(3) = 125(3) + 50 = 425
So f(3) = 425. Now, we already know that x is the time in hours and y, or f(x), is the elevation in feet. We set x to 3 when solving for f(3). We have also found that f(3), or y when x = 3, is 425. So f(3), or 425, is the elevation after 3 hours.
I hope you find my answer and explanation to be helpful. Happy studying.
The amounts of money Brittany earned each week from babysitting for 5 weeks are $12, $62, $70, $54, and $62. The mean amount earned is $52 and the median amount earned is $62. Identify the outlier and describe how the mean and median are affected by it.
Answers
Answer:
The outlier is $12, results in a decrease in the mean. Outliers have little influence on the median.
If you actually calculate and try and find an outlier, this dataset doesn't have one. But I'm going to assume they're just looking for an extreme number in the set since it clearly says to identify it
The requried outlier is $12 and it significantly affects the mean by lowering it, but it does not affect the median.
What is the median?When a dataset is ordered, the median is the value that is exactly in the middle. It is a measure of central tendency that distinguishes between the lowest and top 50% of data.
Here,
The outlier in this data set is the first observation of $12, which is significantly lower than the rest of the values.
The mean is calculated by adding all the values and dividing by the number of values. In this case, the mean is:
$12 + $62 + $70 + $54 + $62 = $260
$260 ÷ 5 = $52
When the outlier of $12 is included in the calculation, it significantly lowers the mean.
The median is the middle value when the data set is arranged in order from least to greatest. In this case, the median is $62, which is not affected by the outlier of $12.
Therefore, the outlier is $12 and it significantly affects the mean by lowering it, but it does not affect the median.
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A body of 60000g is moved through a distance of 8m. Calculate the work done. [take g=10m/s^2]
Answers
Answer:
8m=10m
Step-by-step explanation:
Jan created a garden that was 8.5 yards long and 5.95 yards wide. What is the difference between the length and width of the garden? please dont take my points, actually answer the question.
Answers
Subtract the width from the length.
8.5 - 5.95 = 2.55 yards
Find each value given the following function:
Answers
Answer:
Step-by-step explanation:
1) f(-4) --> if x < or equal to 3
2) 1/(-4)-4
3) The answer is - 1/8
How many possible outcomes exist? 2 3 5 6
Answers
Answer:
1.) C2.) C3.) D4.) D5.) C
Step-by-step explanation:
. Simplify;2 - 2+5 - 2 - 8 -8.
Answers
The given expression:
\(\frac{4}{9}z-\frac{3}{9}z+5-\frac{5}{9}z-8\)To simplify the expression :
Group the similar terms together :
\(\frac{4}{9}z-\frac{3}{9}z+5-\frac{5}{9}z-8=\frac{4}{9}z-\frac{3}{9}z-\frac{5}{9}z+5-8\)
Simplify the similar terms together :
\(\begin{gathered} \frac{4}{9}z-\frac{3}{9}z+5-\frac{5}{9}z-8=\frac{4}{9}z-\frac{3}{9}z-\frac{5}{9}z+5-8 \\ \frac{4}{9}z-\frac{3}{9}z+5-\frac{5}{9}z-8=(\frac{4}{9}z-\frac{3}{9}z-\frac{5}{9}z)+5-8 \\ LCM\text{ of 9,9,9 is 9 So:} \\ \frac{4}{9}z-\frac{3}{9}z-\frac{5}{9}z=\frac{4-3-5}{9}z \\ \frac{4}{9}z-\frac{3}{9}z-\frac{5}{9}z=\frac{-4}{9}z \\ \text{Substitute the value of fraction addition:} \\ \frac{4}{9}z-\frac{3}{9}z+5-\frac{5}{9}z-8=-\frac{4}{9}z+5-8 \\ \text{ Since, 5-8= (-3)} \\ \frac{4}{9}z-\frac{3}{9}z+5-\frac{5}{9}z-8=-\frac{4}{9}z-3 \end{gathered}\)
So, :
\(\frac{4}{9}z-\frac{3}{9}z+5-\frac{5}{9}z-8=-\frac{4}{9}z-3\)
Answer :
\(\frac{4}{9}z-\frac{3}{9}z+5-\frac{5}{9}z-8=-\frac{4}{9}z-3\)
If HI = JK , what is the length of HK ?
Answers
3x-4=x+2
2x=6
x=3
HK=HI+IJ+JK
HI=3.3-4=5
IJ=7.3-9=12
JK=3+2=5
HK=5+12+5=22
pls answer this!!!
worth 30 points
find the circumference of a circle with d=97cm diameter
round to 3 significant figures
Answers
The circular is around 305 cm in circumeference.
The circumference of a circle is given by the formula:
C = πd
where d is the diameter of the circle.
Substituting d = 97 cm and using the value of π to be 3.14159, we get:
C = πd
C = 3.14159 × 97 cm
C ≈ 304.731 cm
Rounding this to 3 significant figures, we get:
C ≈ 305 cm
Therefore, the circumference of the circle is approximately 305 cm.
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7 more than a number ?
A)n+7
B)7+n
C)7-n
Answers
Answer:
B)7+n
Step-by-step explanation:
Answer:
A but see below.
Step-by-step explanation:
A is likely the best answer, although B is also correct. However you should write things in the other they are given.
n + 7 is the very best way to answer.
7 + n is not wrong but maybe not wanted.
evaluate - \(6^{2}- 2(5+1+3\)
Answers
The expression 6² - 2(5 + 1 + 3) after evaluation gives 18.
What is BODMAS rule?BODMAS rule is rule for operation of numbers in a specific order when more than one type of operations is involved.
BODMAS is the abbreviated form for Brackets, Order including powers and exponents, Division, Multiplication, Addition and Subtraction.
Given expression is, 6² - 2(5 + 1 + 3).
First we should do the operation in brackets.
6² - 2(5 + 1 + 3) = 6² - 2 (9)
Now we should do the power operations.
6² - 2 (9) = 36 - 2 × 9
Now we do multiplication.
36 - 2 × 9 = 36 - 18
Now we do subtraction.
36 - 18 = 18
Hence the answer of the expression given is 18.
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2x2 =4 this is 4 or 3 ??????????
Answers
Answer:
4 is the right answer2 × 2 = 42 × 1 = 2 2 × 2 = 42 × 3 = 6 2 × 4 = 82 × 5 = 102 × 6 = 122 × 7 = 142 × 8 = 162 × 9 = 182 × 10 = 20Why is 2+2=4 and 2x2=4? Originally Answered: why does 2*2=4 and 2+2=4? The truth is that a number multiplied by itself does not have to be equal to the same number added to itself. We can prove 2x2=4 easily. We have 2 groups of 2s.Answer:
4 is the right answer......Determine whether the correlation coefficients show strong, moderate, or weak correlation.
Strong Correlation
Moderate Correlation
r=-0.91
r=0.82
r=-049
r=026
r=0.54
r=-0.18
Intro
Weak Correlation
Done
Answers
Answer:
-0.91 = strong, as it is close to -1 and if it's close to -1 that means it is linear.
0.82 = strong. Again, it's approaching 1 and is, therefore, approaching linearity.
-0.49 = moderate
0.26= weak
0.54 = moderate
-0.18 = weak
Step-by-step explanation:
What is the domain and range of each relation
Answers
Answer:
1 ans
domain=(-2,0,2,4)
range=(-3,-1,0)
2 ans
domain=(-3,-1,0,3)
range=(-1,0,1,2,3)
Step-by-step explanation:
Carol and Peter walk to school. Carol walks 3/5 of a mile to walk to school,
Peter walks 0.65. Which student has a father walk?
Answers
For Carols situation, I divided one mile into 5 parts. 1 mile divided by 5 equals .2 miles. Since she walked 3/5 of a mile, I multiplied .2 with 3 which equals 0.6. Carol walked 0.6 Miles.
Peter walked 0.65 mile, so he walked .05 miles farther then Carol
Peter had a farther walk
- If the difference of 15 and a number is 5, what is the number?
Answers
Answer:
The difference of 15 and a number is 5 indeed 10 to be 15
Answer:
10
Step-by-step explanation: